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Properties

Label 34848.2.a.gh
Level $34848$
Weight $2$
Character orbit 34848.a
Self dual yes
Analytic conductor $278.263$
Dimension $6$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [34848,2,Mod(1,34848)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("34848.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(34848, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 34848 = 2^{5} \cdot 3^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 34848.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,0,0,-5,0,-5,0,0,0,0,0,2,0,0,0,0,0,6,0,0,0,-4,0,7,0,0,0,-5, 0,17,0,0,0,2,0,-8,0,0,0,10,0,8,0,0,0,-12,0,5,0,0,0,-9,0,0,0,0,0,-23,0, -8,0,0,0,10,0,24,0,0,0,-30,0,-1,0,0,0,0,0,-23,0,0,0,-25,0,-20,0,0,0,-22, 0,30,0,0,0,26,0,-3,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(278.262680964\)
Dimension: \(6\)
Coefficient field: 6.6.66590000.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{6} - 2x^{5} - 14x^{4} + 30x^{3} + 30x^{2} - 60x - 5 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 6 q - 5 q^{5} - 5 q^{7} + 2 q^{13} + 6 q^{19} - 4 q^{23} + 7 q^{25} - 5 q^{29} + 17 q^{31} + 2 q^{35} - 8 q^{37} + 10 q^{41} + 8 q^{43} - 12 q^{47} + 5 q^{49} - 9 q^{53} - 23 q^{59} - 8 q^{61} + 10 q^{65}+ \cdots - 3 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.